Question

what are matrices?

Answer 1

A is a 2 by 2 matrix \[\textbf A_{22}=\begin{pmatrix}\ a_{11} &a_{12}\\ a_{21}&a_{22} \end{pmatrix}\]

Answer 2

oh, ok

Answer 3

X is a 2 column row vector \[X=(x_1,x_2)\]

W is a 2 row, column vector
\[W=\begin{pmatrix} \ w_1\\w_2\end{pmatrix}\]

scalars are a subset of vectors, which are a subset of matrices

Answer 4

ok, i think i get it. Thanks :)

Answer 5

you can only add/take away matrices that have the same dimensions

Answer 6

dimensions as in same number of rows and columns, or......?

Answer 7

yeah , that is right

Answer 8

ok. So how do you add/subtract them?

Answer 9

\[\textbf A_{22}=\begin{pmatrix}\ a_{11} &a_{12}\\ a_{21}&a_{22} \end{pmatrix}\]
\[\textbf B_{22}=\begin{pmatrix}\ b_{11} &b_{12}\\ b_{21}&b_{22} \end{pmatrix}\]

\[\textbf A_{22}+\textbf B_{22}=\begin{pmatrix}\ a_{11}+b_{11} &a_{12}+b_{12}\\ a_{21}+b_{21}&a_{22}+b_{22} \end{pmatrix}=\textbf C_{22}\]

Answer 10

\[\textbf A_{22}-\textbf B_{22}=\begin{pmatrix}\ a_{11}-b_{11} &a_{12}-b_{12}\\ a_{21}-b_{21}&a_{22}-b_{22} \end{pmatrix}=\textbf D_{22}\]

Answer 11

to add matrices simply add the corresponding elements

Answer 12

do you think you could do it with numbers instead of letters please? sorry, i just would like an example

Answer 13

yeah sure

Answer 14

thanks

Answer 15

\[\textbf M_{22}=\begin{pmatrix}\ 1 &0\\ 6&3 \end{pmatrix}\]
\[\textbf N_{22}=\begin{pmatrix}\ 22 &-8\\ 5&3 \end{pmatrix}\]

\[\textbf M_{22}+\textbf N_{22}=\begin{pmatrix}\ 1+22 &0-8\\ 6+5&3+3 \end{pmatrix}\qquad=\begin{pmatrix}\ 23 &-8\\ 11&6 \end{pmatrix}\]

Answer 16

ohhh, so u add the ones in the corresponding positions?

Answer 17

\[\textbf P_{23}=\begin{pmatrix}\ 5 &1&-3\\ -5&2&4 \end{pmatrix}\qquad \textbf Q_{23}=\begin{pmatrix}\ 0 &0&6\\ 4&2&11 \end{pmatrix}\]

\[\textbf P_{23}-\textbf Q_{23}=\begin{pmatrix}\ 5-0 &1-0&-3-6\\ -5-4&2-2&4-11 \end{pmatrix}=\begin{pmatrix}\ 5&1&-9\\ -9&0&-7 \end{pmatrix}\]

Answer 18

yeah for addition and subtracting just add/subtract the elements in corresponding positions ,
not very difficult

Answer 19

but it only makes sense if the matrices have the same number of columns and rows are each other

Answer 20

ok

Answer 21

thanks :)

Answer 22

any more questions ?

Answer 23

i don't think so

Answer 24

is there any more to matrices than that?

Answer 25

multiplication is trickier ,

there are whole courses on linear algebra
(lots to learn)

conceptually a matrix is like system of equations ,

Answer 26

oh, ok